There has been increasing interest in the measurement, using an acoustic intensity probe, of sound fields radiated into a medium from various acoustic sources. As a consequence, there has also been increased interest in measuring structure-borne intensities (power flows) within the sources.
Several papers have been published which discuss the measurement of structural intensities in thin plates. See Pavic, Proceedings of the International Conference on Recent Developments in Acoustic Intensity Measurement, ed. by M. Crocker, et al. (CETIM, Senis, France 1981), pp. 209-215; Pinnington, et al., ibid., pp. 229-236; Pavic, "Measurement of structure borne wave intensity, part I: Formulation of the methods," J. Sound Vib., Vol. 49, pp. 221-230 (1976); Noiseux, "Measurement of power flow in uniform beams and plates," J. Acoustic Soc. Am., Vol. 47, pp. 238-247 (1970); and Rasmussen, "Measurement of plate waves," J. Acoustic Soc. Am., Vol. 75 (S1), S1(A) (1984). The Noiseux measurement method uses a biaxial accelerometer for measuring intensity in a plate. The Rasmussen method uses two closely spaced accelerometers.
The use of contact accelerometers to measure structural intensity has a number of disadvantages. First, the accelerometers are sensitive to motions in directions perpendicular to the desired measurement direction. This is especially a problem when the accelerometers are used in a biaxial or triaxial configuration. In addition, the weight and rotational inertia of the accelerometers can interfere with the vibration of the plate, and thus with calculation of the intensity measurements. Further, the amplitude and phase responses of the accelerometers must be very closely matched in order to ensure accurate measurements. In some cases, phase matching of 0.1 degrees is required.
A number of measurement methods have been used which provide diverse information about the radiation of sound waves from a source. These are generally concerned with providing one of the following characteristics of the sound field: farfield directivity, nearfield vector intensity, surface velocity (as for a vibrating plate), and total sound power. To measure the farfield directivity, a microphone in the farfield is passed around a sound source in an anechoic chamber to determine the variation of the sound pressure with respect to the angle between the microphone and the sound source. These measurements are used in underwater source calibrations, in loudspeaker and musical instrument studies, and the like. A disadvantage of farfield directivity measurements is that large or low frequency sources require the microphone to be placed a considerable distance away from the source to get an accurate measurement, which may be beyond the size of any available anechoic chamber. There are other techniques which use measurements in the near field on cylindrical and spherical surfaces to calculate the far field directivity. For these measurements, a small anechoic chamber is sufficient, but an anechoic chamber is still required.
Measurement of the nearfield vector intensity has received a great deal of attention in acoustics. U.S. Pat. No. 3,364,461 to W. J. Trott discloses a large planar array of transducers wherein the sensitivities of the individual elements (transducers) are shaded to produce a constant, planar wave in the nearfield extending over the aperture of the array. The shading is such that the sensitivity of the elements increases from the extremities toward the center of the array according to the coefficients of a summed binomial probability distribution function. While this system provides nearfield measurements over a large aperture, and the simultaneous outputs of the elements are integrated to provide some useful response and directivity characteristics of a sound source, it has the disadvantage of relatively fixed shading values, and lacks the ability to resolve the individual radiating features of a complex source.
In another technique, two closely spaced microphones are moved in an imaginary surface enclosing a sound source to measure both the sound pressure and its gradient. From such measurements, one component of the vector intensity may be calculated. By scanning over a surface, the average radiant sound power can be determined. This technique is limited, though, because coherent measurement can be made only in a small area, and the results do not reveal the complicated nature of the intensity vector field in the vicinity of the source, nor the transition region between the source and the farfield. There is further error due to the finite separation of the microphones. Another common intensity measurement technique is similar to the two microphone technique, but uses an accelerometer mounted to the source in place of the second microphone. The accelerometer determines the component of the pressure gradient normal to the surface, and hence only determines the normal component of the intensity. The single microphone/accelerometer technique suffers from the same disadvantages as the two microphone technique, and is also time consuming for larger, more complicated sources. The surface velocity, or modal pattern, is usually determined by mapping the surface with an accelerometer, but like the two microphone intensity measurement technique, this has a disadvantage of being time consuming. A known non-contact method of determining the surface velocity involves optical holography. This technique, however, requires highly specialized equipment and controlled laboratory conditions, and cannot be used to study large areas.
The present inventor is also the coinventor of a nonwavelength-limited method of holographic reconstruction of sound fields to provide visual representations of acoustical characteristics of sound waves, which method is disclosed in U.S. Pat. No. 4,415,996 to Maynard et al. and assigned to the assignee of the present invention.